Area of intrinsic graphs in homogeneous groups

TL;DR

This paper develops an area formula for intrinsic graphs in homogeneous groups, introducing a new Jacobian concept based on an auxiliary scalar product, under the assumption of continuous intrinsic differentiability.

Contribution

It provides the first area formula for intrinsic graphs of any codimension in homogeneous groups using a novel Jacobian definition.

Findings

Established an area formula for spherical measure of intrinsic graphs

Introduced a new Jacobian based on an auxiliary scalar product

Applicable to intrinsic graphs of any codimension in homogeneous groups

Abstract

We establish an area formula for the spherical measure of intrinsic graphs of any codimension in homogeneous groups. Our approach relies on the assumption that the map defining the intrinsic graph is continuously intrinsically differentiable. The main novelty is a notion of Jacobian defined using an auxiliary scalar product.